Numerical experiments for acoustic modes of a square cavity using the dual boundary element method

Abstract

The dual integral formulation for the Helmholtz equation for use in solving the acoustic modes of a two-dimensional square cavity is derived, and a general dual boundary element method (BEM) program is developed. Numerical experiments for the degenerate acoustic modes of a square cavity are performed. It is found that the degenerate modes can be distinguished by specifying the normalized boundary data at different boundary points using either the singular integral equation (UT method) or the hypersingular integral equation (LM method). This technique can be employed to determine the multiplicity of the eigenvalue. Two examples with Dirichlet and Neumann boundary conditions are given to show the validity of the proposed technique. Sensitivity and failure in determining the acoustic modes by specifying the normalized data at the boundary locations near and on the node are examined, respectively. Also, numerical results are obtained using finite element method (FEM) and analytical solutions for comparison. Good agreement between them is obtained.